19 citations · 109 across the 25 of their papers we have counts for
30 papers
Excursion Fluctuations and Spectral Universality in Gaussian Fields
Dmitry Beliaev, Akshay Hegde
We study the large-scale spatial fluctuations of excursion volumes for a class of smooth stationary Gaussian fields. In the case of Berry's random wave model in dimension $d \geq 2…
High local maxima of stationary smooth Gaussian fields
Dmitry Beliaev, Akshay Hegde
Consider the point process (in ) of local maxima of smooth Gaussian fields, with sufficient decay of correlation at infinity, above a level . We show that this poi…
A covariance formula for the number of excursion set components of Gaussian fields and applications
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on contained in compact domains. We also pre…
On convergence of volume of level sets of stationary smooth Gaussian fields
Dmitry Beliaev, Akshay Hegde
We prove convergence of Hausdorff measure of level sets of smooth Gaussian fields when the levels converge. Given two coupled stationary fields , we estimate the differe…
Gaussian fields and percolation
Dmitry Beliaev
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large sc…
A central limit theorem for the number of excursion set components of Gaussian fields
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
For a smooth stationary Gaussian field on and level , we consider the number of connected components of the excursion set (or l…